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HST.187: Physics of Radiation Oncology #9. Radiation therapy: optimization in the presence of uncertainty Alexei Trofimov, PhD Jan Unkelbach, PhD Dept of Radiation Oncology MGH April 3, 2007

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Uncertainties in RT Intro –Sources of uncertainty, e.g. - Set-up, target localization (inter-fractional) Intra-fractional motion –Methods to counter the uncertainties Volume definitions/ margins, treatment techniques –Effect of uncertainties on the dose distribution Probabilistic planning techniques in the presence of uncertainties –Inter-fractional motion and set-up uncertainties –Proton range variations in tissue Handling of intra-fractional motion (respiratory) –Image-guided radiation therapy IGRT and “4D” planning –Probability-based motion-compensation –Intro to robust optimization

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Target definition: inter-observer variation Steenbakkers et al R&O 77:182 (2005)

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Target motion (intra-fractional) Targeting

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Interplay between internal motion and the multi-leaf collimator sequence JH Kung P Zygmanski

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Target motion (intra-fractional) Targeting Radiological depth changes InhaleExhale

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Planned dose at exhale phase Liver Tx plan, PA field Planned by J.Adams (TPS: CMS XiO) As would be delivered at inhale 50%

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Set-up uncertainties: day-to-day variation Images: © 2007 Elsevier Inc Zhang et al IJROBP 67:620 (2007) Variation over 8 weeks of treatment

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Prostate treatment with protons

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Compensator design

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Variation In set-up

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Compensator smear

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Compensator smear

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Intrafractional motion

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Part 2: Probabilistic approach to account for uncertainty in IMRT/IMPT optimization

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Content Motivation – interfractional random setup error Concept of probabilistic treatment planning Application to interfractional motion of the prostate Application to range uncertainties in IMPT

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Motivation Consider inter-fractional random setup error in a fractionated treatment How can we achieve an improvement? Lower dose to regions where tumor is located rarely Have to compensate for it by higher dose to other regions safety margin: irradiate entire area where tumor may be with the full dose

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Motivation 25 moving voxels 45 static voxels Example: Question? Are there static dose fields that yield tumor coverage and improve healthy tissue sparing? tumor voxels are at 5 different positions equally often

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Motivation Example: integral dose: 40.8 (instead of 45.0)

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Motivation Dose in the moving tumor: frequency for moving voxel i being at static voxel j Have to solve system of linear equations to determine static dose field which yields D = 1 dose in moving tumor static dose field

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Motivation special solution (safety margin) Set of solutions is affine subspace kernel of the mapping P: Set of static dose fields which preserve D = 1: kernel dimension (number of static voxels) minus (number of tumor voxels)

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Motivation Intrinsic problems: only handles predictable motion, not uncertainty cannot handle systematic errors cannot handle irreproducable breathing pattern Method could in principle work if motion was predictable and treatment was infinitely long Need more general method to handle uncertainty! (having these ideas in mind)

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Idea of probabilistic method Main assumption: The dose delivered to a voxel depends on a set of random variables vector of random variables which parameterize the uncertainty fluence map to be optimized Assign probability distribution to random variables:

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Idea of probabilistic method Applications: G = position of voxels P(G) = Gaussian distribution Inter-fractional motion range uncertainty respiratory motion G = amplitude, exhale position, starting phase (note: P(G) unrelated to `breathing PDF`) G = range shifts for all beamlets

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Idea of probabilistic method Postulate: optimize the expectation value of the objective function incorporate all possible scenarios into the optimization with a weighting that corresponds to its probability of occurrence

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Idea of probabilistic method Example: quadratic objective 1st order term2nd order term variance of the dosedifference of expected and prescribed dose expected dose:

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Alternative formulations In this talk: optimize expectation value most desireable might be something in between (can be solved by robust optimization techniques in linear programming) alternative: optimization of the worst case

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Application to prostate Incorporating inter-fractional motion of the prostate into IMRT optimization

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application to prostate Uncertainty G: positions of voxels Probability distribution P(G): Gaussian

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application to prostate static dose field (dose per fraction) expected quadratic objective function 30 fractions large amplitude of motion ( 8mm AP, 5mm LR/CC)

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application to prostate expected dose in the moving tumor coordinate system Best estimate for the dose delivered to a voxel

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application to prostate Problem: Uncertainty implies that we don‘t know the dose distribution which will be delivered standard deviation: assess uncertainty of the dose in each point treatment plan evaluation difficult

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application to prostate Probability for the delivered dose to be below/within/above a 3% interval around the prescribed dose belowabovewithin (D Maleike, PMB 2006)

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application to prostate Prototype GUI to view probabilities for over/under dosage (D Maleike, PMB 2006) user may select dose intervals of interest

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Application to prostate Incorporate organ motion in IMRT planning to overcome the need of defining safety margins resemble the idea of inhomogeneous dose distributions on static targets in order to achieve better healthy tissue sparing control the sacrifice of guaranteed tumor homogeneity Probabilistic approach can...

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Application to range uncertainties Handling range uncertainty in IMPT optimization

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Application to range uncertainties degraded dose distribution if the actual range differs from the assumed range assumed range+ 5 mm - 5 mm Conventional IMPT treatment plans may be sensitive to range variations

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Application to range uncertainties Why? Because... pencil beams stop in front of an OAR dose distributions of individual beams are inhomogeneous

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Application to range uncertainties Range uncertainty assumptions for probabilistic optimization: 5 mm uncertainty (SD) of the bragg peak location for each beam spot Gaussian distribution for the range shifts is considered a systematic error (no averaging over different range realizations in different fractions)

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Application to range uncertainties assumed range+ 5 mm- 5 mm Probabilistic optimization can significantly reduce the sensitivity to range variations convetional plan

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Application to range uncertainties Why? Because... lateral fall-off of the pencil beam is used dose distributions of individual beams are more homogeneous in beam direction convetional plan

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Application to range uncertainties Price of robustness: lateral fall-off is more shallow convetional plan plan quality for the assumed range is slightly compromised - higher dose to OAR or reduced target coverage probabilistic plan

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Application to range uncertainties take advantage of the characteristic features of the proton beam and the many degrees of freedom in IMPT to make treatment plans robust with respect to range variations (which cannot be achieved by other known heuristics) Probabilistic approach can...

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Part 3: Intrafractional motion

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Continuous irradiation

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IMRT delivery to a moving target Int map no motion motion 1 fraction motion 4 fx

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The effect of target motion on dose distribution

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Coverage assured with planning margins

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Gated Tx at MGH Varian RPM-system marker block with IR-reflecting dots IR-source + CCD camera

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External-internal correlation Tsunashima et al IJROBP 2003

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Gierga et al IJROBP 2004: correlation differs between markers

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Phase shift H Hoisak et al IJROBP 2003

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External-internal correlation Generally well-correlated, but… Not necessarily linear Phase shift has been observed, not necessarily constant on different days Proportionality coefficients, phase may vary with –marker position –respiratory “discipline” (e.g. compliance with breath- training/coaching)

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(“Fast”) tracking delivery

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Inverse optimization Dose calculation using (D ij ) matrix: beamlet j x voxel i

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4D- influence matrix (D-ij) approach D ij ’s are precalculated for all beams and all instances of geometry (4D-CT phases) At instance (phase) k we have k = 1, …, 5: breathing phase beamlet j x voxel i

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Eike Rietzel, GTY Chen “Deformable registration of 4D CT data” Med Phys 33:4423 (2006) Determine voxel displacement vector field between Pk and P0 (reference phase) P0 (inhale) P4 (exhale)

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Deformations are then applied to all pencil beams in D ij matrix pencil beam in P4 (exhale) same pencil beam transformed to P0 (inhale) x x A Trofimov et al PMB 50:2779 (2005)

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Continuous irradiation: instantaneous dose distribution

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From a different prospective: a moving instant. dose in a fixed reference geometry

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Approaches to temporo-spatial optimization of IMRT (1) Planning with optimal margins (Internal Target Volume) (2) Planning with Motion kernel (a)Uniform approach (motion PDF) (b)Adaptive approach (sum influence matrix) (3) Gating / Unoptimized tracking – plans optimized separately, 1 best plan chosen out of several or all delivered dynamically (4) Optimized tracking – several plans optimized simultaneously, delivered dynamically A Trofimov et al PMB 50:2779 (2005)

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Lung: CTV vs Internal Target Volume (ITV)

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Planning with “Internal” margins - ITV

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App. 1: Optimal margins (ITV): lung

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DVH for ITV plan recalculated for different geometries (CT phases): lung

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Approaches to Temporo-Spatial Optimization of IMRT (1) Planning with expanded margins (ITV) (2) Planning with modified dose kernel (b) Uniform approach (motion PDF) (a)Adaptive approach (sum influence matrix) (3) Gating / Unoptimized tracking – plans optimized separately, 1 best plan chosen out of several or all delivered dynamically (4) Optimized tracking – several plans optimized simultaneously, delivered dynamically

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Motion probability distribution function (PDF)

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Motion-compensation in IMRT treatment planning If the motion (PDF) is known (reproducible), the dosimetric effect can be reduced – Deconvolution of intensity map – Planning with “smeared” beams –.

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Reduction of integral dose with motion-adaptive planning

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. Motion kernel: “one-size-fits-all” vs. “custom-made” Original beamlet = Convolved “motion” beamlet Sum of deformed beamlets

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IMRT with motion-compensated Tx Plan Int map no motion motion 1 fraction motion 4 fx

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Patient data lung liver

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App. 2a: Motion kernel plan, DVH recalculated for 5 ph’s

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MK plan: DVH recalculated for diff phases

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App. 2b: with averaged Dij-matrices (liver)

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Inhale (recalc’d to reference)Exhale (reference) Inhomogeneous “per-phase” doses are designed so that the some conforms to the prescription

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Approaches to Temporo-Spatial Optimization of IMRT (1) Planning with expanded margins (ITV) (2) Planning with modified dose kernel (Motion kernel) (a)Uniform approach (motion PDF) (b)Adaptive approach (sum influence matrix) (3) Gating / Unoptimized tracking – plans optimized separately, 1 best plan selected for gated delivery or all delivered dynamically (4) Optimized tracking – several plans optimized simultaneously, delivered dynamically

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App. 3: Gating / Unoptimized tracking (liver)

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App. 3: Gating / Unoptimized tracking (lung)

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Approaches to Temporo-Spatial Optimization of IMRT (1) Planning with optimal margins (ITV) (2) Planning with modified dose kernel (Motion kernel) (a)Uniform approach (motion PDF) (b)Adaptive approach (sum influence matrix) (3) Gating / Unoptimized tracking – plans optimized separately, 1 best plan selected for gated delivery or all delivered dynamically (4) Optimized tracking – several plans optimized simultaneously, delivered dynamically

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App. 4: optimized tracking (lung)

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App. 4: Optimized tracking (lung)

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DVH comparison for the lung case

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DVH comparison for liver case

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Ideal case for tracking delivery (vs gating)

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DVH and dose for different “gated” (single phase) plans for the lung case

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Sources of delay: RPM: ms, 75 ms average System response time : < 5 ms Wait for the next modulation cycle: ms Total delay: ms, average 130 ms Delivery of gated proton treatment : Timing Delivery restricted to complete modulation cycles: on/off at the stop block position only 100 ms Hsiao-Ming Lu

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Residual motion with gating Probability distribution

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Inter-fractional variability Liver-2

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Cardiac-1

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Cardiac-2

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Cardiac-1 Time Position

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Variability between patients Lung-2 Liver-2Cardiac-2

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Robust formulation for probabilistic treatment planning: –Tim Chan et al: Phys Med Biol 51:2567 (2006) –Outcome will be “acceptable” as long as the realized motion is within the expected “limits”

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PDF uncertainty bounds Realized PDF Planning PDF Dose to moving target

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Summary (Some) sources of uncertainty in RT: imaging, target definition, dose calc, set-up, inter-, intra-fractional motion Margin/ITV approach is the most robust for target coverage, but substantially increases dose to healthy tissue Image-guided RT improves dose conformity, reduced irradiation of healthy tissues, BUT relatively complex delivery, not error-proof Probabilistic motion-adaptive treatment planning in combination with image-guided delivery may be the optimal solution

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Acknowledgements J Adams T Bortfeld, PhD T Chan, PhD S Jiang, PhD J Kung, PhD HM Lu, PhD H Paganetti, PhD E Rietzel, PhD C Vrancic

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